eTwinning project

1. PI DAY
Covering a flower pot
We measured the circumference and height of a few pots of flowers in our
school. We want to cover the lateral surface of the pot with a decorative
paper. What surface should have the decorative paper for this action?
We obtained the circumference of the great circle 𝑳 𝟏 = 𝟏𝟐𝟔 𝒄𝒎
We obtained the circumference of the little circle 𝑳 𝟐 = 𝟔𝟑 𝒄𝒎
Height of the pot is h=40 cm
𝑳 𝟏 = 𝟐𝝅𝑹 ⟹ 6,28 ⋅ 𝑅 = 126
⟹ 𝑅 ≃ 20,06 ≈ 20 ⟹
⟹ 𝑹 ≈ 𝟐𝟎 𝒄𝒎
𝑳 𝟐 = 𝟐𝝅𝒓 ⟹ 6,28 ⋅ 𝑟 = 63
⟹ 𝑅 ≃ 10,03 ≈ 10 ⟹
⟹ 𝒓 ≈ 𝟏𝟎 𝒄𝒎
𝐶𝐸 ⊥ 𝐴𝐵 ⟹ 𝐺2
= ℎ2
+ (𝑅 − 𝑟)2
⟹
⟹ 𝐺2
= 1600 + 100 ⟹
⟹ 𝑮 = 𝟒𝟏, 𝟐 cm ⟹ 𝑨𝒍 = 𝝅𝑮(𝑹 + 𝒓) ⟹ 𝑨𝒍 = 𝟑, 𝟏𝟒 ⋅ 𝟒𝟏, 𝟐(𝟐𝟎 + 𝟏𝟎)
𝑨𝒍 = 𝟑𝟖𝟖𝟏 𝒄𝒎 𝟐

2. The radius of the cone which result from the truncated
con is R=10.
Lateral surface of the cone in which the trunk of cone
is a circular sector with radius as the cone generator R.
We must calculate the measure of the angle of the
cicular sector 𝑚(∡𝐴𝑉𝐴") = 𝑛°
.
Lateral surface of the truncated cone is a circular
crown. The areaof the circular crown is 3881.
𝑉𝐴
𝑉𝐶
=
𝑟
𝑅
=
1
2
⟹ 𝑉𝐴 = 𝐴𝐶 = 41,2 ⟹ 𝐶𝑉 = 82,4 ⟹
The length of circular arc is 𝐿 =
𝜋𝑅𝑛∘
180∘
, where R=CV
⟹
𝜋∙82,4∙𝑛∘
180∘
= 126 ⟹ 𝑛°
=
126∙180°
82,4𝜋
⟹ 𝑛°
≈ 88°
.
Considering the joints, we need
𝑛°
≈ 90°
.
The area of MCVC’ is the area of a
square.
A=l2
=6790 cm2
=0,679m2
.
So we need 0,7 m2
paper for our pot.
Andra Pitiș, Ann Miess Chisthine – clasa a VIII-a B